Table 8.9
The manager of a pizza shop must forecast weekly demand for special pizzas so that he can order pizza shells weekly. Recent demand has been:

WEEK No. Special Pizzas
1 30
2 45
3 33
4 36
5 35
6 40

Use the information from Table 8.9. The pizza shop manager believes that a combination forecast might improve her ability to predict future demand, and thus improve keeping fresh ingredients on hand. She decides to use the 3-week weighted moving average and exponentially smoothed average forecast, giving them equal weight. The 3-week weighted moving averages are .6 for the most recent period, .25 for the second most recent period, and .15 for the third most recent period. The smoothing constant is .10 and the previously forecasted demand for week 6 was 39.28 pizzas. What is her forecast for week #7?

Question

Table 8.9
The manager of a pizza shop must forecast weekly demand for special pizzas so that he can order pizza shells weekly. Recent demand has been:

WEEK	No. Special Pizzas
1	30
2	45
3	33
4	36
5	35
6	40

Use the information from Table 8.9. The pizza shop manager believes that a combination forecast might improve her ability to predict future demand, and thus improve keeping fresh ingredients on hand. She decides to use the 3-week weighted moving average and exponentially smoothed average forecast, giving them equal weight. The 3-week weighted moving averages are .6 for the most recent period, .25 for the second most recent period, and .15 for the third most recent period. The smoothing constant is .10 and the previously forecasted demand for week 6 was 39.28 pizzas. What is her forecast for week #7?

BlackTom AI · Accepted Answer

To evaluate the forecast for week 7, we must combine two components with equal weight: a 3-week weighted moving average (WMA) and an exponentially smoothed average forecast (EMA).

Option-by-option analysis:

Option: 42.25 pizzas
- This value would require a combination that yields a result around 42.25, which is notably higher than the recent 3-week weighted average and only modestly above the EMA forecast. If we compute the 3-week WMA from weeks 4–6 with weights 0.15, 0.25, and 0.60, we get 0.60×40 + 0.25×35 + 0.15×36 = 24 + 8.75 + 5.4 = 38.15. The EMA forecast for week 7 uses F7 = F6 + α(A6 − F6) with F6 = 39.28 and α = 0.10, so F7 = 39.28 + 0.10×(40 − 39.28) = 39.28 + 0.072 = 39.352. Averaging 38.15 and 39.352 gives about 38.75, far from 42.25. Therefore, this option is inconsistent with the stated equal-weight combination method.

Option: 44.8 pizzas
- Getting 44.8 would require a much larger contribution from the 3-week WMA or EMA than what the data support. As shown above, the 3-week WMA is 38.15 and the EMA forecast is 39.352; averaging these cannot reach anywhere near 44.8. Thus, this choice does not align with the prescribed calculation.

Option: 38.75 pizzas
- This value exactly matches the result you'd obtain by taking the average of the 3-week weighted moving average (38.15) and the exponentially smoothed forecast (39.352): (38.15 + 39.352) / 2 ≈ 38.751, which rounds to 38.75. The steps used—computing the WMA with weights 0.60, 0.25, 0.15 on weeks 6, 5, and 4 respectively, and updating the EMA with α = 0.10 from F6 = 39.28 and A6 = 40—produce this combined forecast when the two components are equally weighted.

Option: 40.8 pizzas
- A forecast of 40.8 would require more influence from the EMA than the WMA in the equal-weight scheme, or a miscalculation of the EMA step. But with the EMA computed as 39.352 and the WMA at 38.15, the simple average yields about 38.75, not 40.8. Therefore this value does not follow from the stated method.

Summary of the reasoning flow:
- Compute the 3-week weighted moving average using weeks 6, 5, and 4 with weights 0.60, 0.25, and 0.15 respectively, giving 38.15.
- Compute the exponentially smoothed forecast for week 7: F7 = 39.28 + 0.10×(40 − 39.28) = 39.352.
- Form the equal-weight combination forecast: (38.15 + 39.352) / 2 ≈ 38.751, which rounds to 38.75.
- Compare each option to these computed values: only 38.75 aligns with the equal-weight combination result, while the others deviate due to either overemphasizing one component or stemming from arithmetic missteps.

MGS310001.2025FA Test 02: Chapter 5, 8, 9

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类似问题

Which of the following forecasting methods requires the least amount of past data to produce a forecast for the next period?

With the multiplicative seasonal method of forecasting:

Time-series forecasting takes into consideration historical data and the influence of other internal and external factors likes sales promotions and economic indicators to compute a future forecast.

A naive forecast is a time-series method whereby the forecast for the next period equals the demand for the current period.

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MGS*3100*01.2025FA Test 02: Chapter 5, 8, 9